Certain physical laws have been predicted theoretically before being verified experimentally. But historically, this is not the case of the most widely used law in chemical kinetics: the Arrhenius constant, which has been laboriously constructed to best fit to chemical transformations [1]}. The subject of this paper is precisely to imagine how the current form of rate constants might have been predicted before undertaking experimental tests. Such a theoretical exercise is of course easier when the expected result is already know, but it will nevertheless prove of pedagogical interest and useful for reconsidering rate theories. The classical form of the Arrhenius law was published in 1889 [2]} and anticipated by van't Hoff in 1884 [3]}, but van't Hoff acknowledged that he did not enter into theoretical considerations [3]}. This equation related to temperature through the Boltzmann factor, has proved very effective for modeling chemical reactions, but also simple experiments unrelated to chemistry such as a mechanical simulator allowing one to count the passages of a randomly propelled ping-pong ball between two different levels of a plateau [5]}. Several attempts of formalization have been developed a posteriori, based on thermodynamics, statistical mechanics and quantum mechanics, including diffusion from an energy well [6]}, reactive flux [7]} and transition path [8]} theories. These different approaches yielded similar formulas, which can of course be explained in part by the will of the authors to recover the efficient general form, but in addition, the same form is obtained for reactions of any order [9]} and the same maximal quantum frequency can be derived as well by envisioning the reaction coordinate as a vibration or as a translation [10]}. This convergence of approaches towards a single general law justifies the Arrhenius law and also suggests the existence of a founder principle reduced to its mathematical essence. Chemical reactions will be conceived as stochastic transitions whose frequency is just determined by the waiting time of two simultaneous favorable conditions, one configurationnal and the other energetic. In practice, reactants must not only be well positioned and oriented for the reaction, but also receive from their environment a sufficient amount of energy, higher than the average ambient energy, which occasionally happens by fluctuations. Remarkably, the simplest and in fact the only rigorous mathematical way of meeting by chance these two conditions, directly gives the law of Arrhenius, thus bypassing more complex theories and making unnecessary some postulates. In particular, this direct construction of the Arrhenius law does not use the chemical intermediate in equilibrium with the reactant called activated complex in the transition state theory (TST), whose existence somewhat breaks the notion of elementary reaction and mixes equilibrium and transient phenomena. The alternative presentation also helps clarifying the different chemical energy values used in rate theories, such as molecular energies and the transition state energy. A primary characteristic of the present proposal is to conform to the concept of unique stochastic chemical event, which is strangely ignored in diffusion, random walk and reaction path theories.
